Question

Алгебра 8 класс,помогите. катер проплывает 20 км против течения и ещё 24км по течению за то же время,за которое плот может проплыть по этой реке 9 км .Скорость катера в стоячей воде равна 15км/ч.Найдите скорость течения реки

Answer 1

Х-скорость течения
15+х скорость катера по течению
15-х его скорость против течения
20/15-х + 24/15+х= 9/х
20х(15+х)+24х(15-х)=9(225-х²)
5х²+660х-2025=0
х²+132х-405=0
Д=132²+4*405=17424+1620=19044=138²
х₁=-132-138/2 отрицательное число не удовл условию
х₂=-132+138/2=3км/ч
ответ: 3 км/ч

Answer 2

Problem Analysis

We are given that a boat can travel 20 km against the current and 24 km with the current in the same amount of time it takes for a raft to travel 9 km on the same river. The speed of the boat in still water is given as 15 km/h. We need to find the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When the boat is traveling against the current, its effective speed is reduced by the speed of the current. So, the boat's speed against the current is 15 - x km/h.

When the boat is traveling with the current, its effective speed is increased by the speed of the current. So, the boat's speed with the current is 15 + x km/h.

We are given that the boat can travel 20 km against the current and 24 km with the current in the same amount of time it takes for the raft to travel 9 km. We can set up the following equation based on the time taken:

20 / (15 - x) = 24 / (15 + x) = 9 / x

To solve this equation, we can use the method of cross-multiplication.

Calculation

Cross-multiplying the first two fractions, we get:

20 * (15 + x) = 24 * (15 - x)

Expanding and simplifying:

300 + 20x = 360 - 24x

Combining like terms:

44x = 60

Dividing both sides by 44:

x = 60 / 44

Simplifying the fraction:

x = 15 / 11

Therefore, the speed of the river's current is 15/11 km/h.

Answer

The speed of the river's current is 15/11 km/h.